[leetbulb]

I have implemented an extremely similar protocol for a side project game.

In my implementation, step 4 happens in two phases:

4a. All members submit their secret values to the server.

4b. Once all secret values are submitted, they are all sent to each member at once.

This ensures that members cannot determine the outcome before anyone else.

What you are describing could actually be an issue if there is no server involved, however something like commitment encryption (rather than hashing) utilizing secret sharing could help resolve this issue in a p2p environment.

Another option would be that all possible outcomes are randomly shuffled with their positions encrypted and distributed to all members prior to the game beginning.

My protocol implements the latter... all possible outcomes are encrypted and publicly available on IPFS to members before and after the game.